Some households could be more than £400 worse off by the end of the decade. Consumer Futures says in a report that home owners are only likely to get the reduced savings if they can afford to replace their household appliances with more “energy efficient’ products.

The official consumer protection body says more than two million low income families will see their annual dual-fuel bills rise by an average of £282 because of ministers’ measures.

Rural households that rely on electricity to heat their homes could be £460 worse off by the end of the decade.

William Baker, the watchdog’s policy lead, said: “We think the Government is being rather optimistic about the level of savings that can be generated.”

Downing Street is ploughing ahead with a range of measures to reduce the country’s carbon levels, through everything from levies to loft insulation.

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Much of the cost is being passed back to households through energy bills. Ed Davey, the Energy Secretary, said in March his policies should ultimately save households as much as £166 a year by 2020. But the Consumer Futures report says the saving is closer to £31 a year.

The group says ministers had forgotten about the effects on homes that rely on electricity for their heating. The watchdog says these homes are bearing much of the cost of the policies but will get little of the benefit. Those forecast to miss out are low income adults living in electrically heated rental houses or tower blocks.

Adam Scorer, Consumer Futures’ director, said: “Most of the policies are funded through electricity bills. Households with electric heating will face a disproportionate share of the costs.”

He added there was a real danger about the Government’s “heroic assumptions” that much of their forecast saving will come from people buying new energy efficient products. Consumer Futures says that if households don’t spend on new goods, bills will actually be £93 higher on average by 2020.

Green fuel policies will cost some families £400 a year, watchdog warnsThe Department of Energy and Climate Change said it stood by its sums.

A spokesman insisted that the £166 was based on the savings generated by green policies in place since 2002. The Consumer Futures study was based on measures introduced after 2010.

But the report’s author Ian Preston said: “Two years ago they were predicting savings of £100. Now it’s £166 and if you look at the Energy Bill they say the amount they are going to spend is going up. There seems to be a disconnect.”